📚 Gujarat TET – Quantitative Aptitude
Topic: Percentages
“Percent” means per hundred.
Think of a pizza divided into 100 equal slices.
If you take 30 slices, you own 30 % of the pizza.
1. What is a Percentage?
| Word | Everyday Analogy | Tiny Example |
|---|---|---|
| Percentage | If you have 100 € in your wallet, 25 € is 25 % of it. | 25 € of 100 € → 25 % |
| Whole | The entire pizza, the full amount of money, the total number of apples. | 100 € |
| Part | The slice you actually eat, the money you spend, the apples you pick. | 25 € |
Key Idea – Percentage tells you how many parts of 100 a number represents.
2. Basic Formula
Percentage = (Part ÷ Whole) × 100
Use a calculator or simple mental math.
Example
You have 30 apples out of a basket of 200 apples.
Percentage of apples you have = (30 ÷ 200) × 100 = 15 %
3. Quick Steps to Find a Percentage
- Identify the part and the whole.
- Divide part by whole.
- Multiply by 100.
- Write the answer with the % sign.
Tip: If the whole is already 100, the answer is just the part.
4. Common Percentage Problems
| Problem | What to Find | Steps |
|---|---|---|
| A. “What is 12 % of 250?” | Part | 12 ÷ 100 × 250 = 30 |
| B. “If 18 % of a class are boys, how many boys are there in a class of 120?” | Part | 18 ÷ 100 × 120 = 21 |
| C. “A price drops from 200 ₹ to 180 ₹. What is the percent decrease?” | Decrease | (200 – 180) ÷ 200 × 100 = 10 % |
| D. “A test score improves from 70 % to 85 %. What is the percent increase?” | Increase | (85 – 70) ÷ 70 × 100 ≈ 21.4 % |
5. Quick Calculation Tricks
| Trick | When to Use | Example |
|---|---|---|
| Use 100 as the whole | When you’re asked for a percentage directly. | 15 % of 300 = 15 ÷ 100 × 300 = 45 |
| Convert to 1/100 | To avoid multiplying by 100 every time. | 25 % = 25 ÷ 100 = 0.25 |
| Cross‑multiplication | When part or whole is missing. | If 20 % of X = 30 → X = 30 ÷ 0.20 = 150 |
6. Tiny Practice Problems
Try solving before checking the answer.
- What is 18 % of 75?
- A book costs ₹500. It is on sale for ₹350. What is the percent discount?
- In a bag of 250 candies, 40 are chocolates. What percent are chocolates?
- A student scores 80 % in the first half of the exam and 90 % in the second half. What is the overall percentage?
Answers
- 13.5
- 30 %
- 16 %
- 85 % (average of two halves)
7. Quick Review Checklist
- Can I identify part and whole?
- Do I remember the formula:
(Part ÷ Whole) × 100? - Can I solve for part, whole, or percentage in one step?
- Do I use the right trick for quick mental math?
Final Thought
Percentages are simply a way to compare a part with a whole using 100 as the reference. Once you practice a few problems, you’ll find them as easy as counting slices of pizza. Happy studying! 🍎✏️